TLDR: A research paper introduces an innovative optimization method for meat processing plants to efficiently manage purchasing and material processing. It addresses unique real-world constraints like minimum order quantities (MOQ) and minimum percentage in alternatives (MPA), which are proven to make the problem computationally challenging (NP-hard). The proposed solution is an iterative Integer Linear Programming (ILP) approach that overcomes numerical instability and allows for quick, optimal solutions using open-source software, significantly improving cost management and adaptability for meat processing companies.
The global food industry, particularly the meat production sector, is currently navigating a complex landscape of challenges. Factors such as the recent energy crisis in the European Union, the COVID-19 pandemic, rising inflation, and increasing energy prices have put immense pressure on companies to operate more efficiently. This environment, coupled with demands for sustainability and a shortage of skilled labor, highlights the critical need for optimized processes to maintain profitability and competitiveness.
A recent research paper, titled “Purchase and Production Optimization in a Meat Processing Plant,” delves into a crucial optimization problem faced by meat processing companies. Unlike many existing studies that focus on broader supply chain management, this paper zeroes in on the intricacies of the production stage itself. The core challenge involves making smart decisions about purchasing raw materials and how these materials are subsequently processed.
The problem is made particularly complex by several real-world constraints often overlooked in academic literature. These include the concept of alternative ways to process materials, managing stock with varying expiration dates, and two significant additional requirements: the Minimum Order Quantity (MOQ) and the Minimum Percentage in Alternatives (MPA). MOQ dictates that if a material is purchased, it must be bought in at least a specified minimum quantity. MPA, on the other hand, requires that if a material from a group of interchangeable alternatives is used in a recipe, it must constitute a minimum percentage of that group’s total quantity, due to practical limitations in industrial-scale production.
The authors of the paper, Marek Vlk, Pˇ remyslˇS˚ ucha, Jaros/suppress law Rudy, and Rados/suppress law Idzikowski, prove that each of these two constraints—MOQ and MPA—individually makes the optimization problem “NP-hard.” This means that finding the absolute best solution becomes incredibly difficult and time-consuming as the problem size grows, even for powerful computers.
To tackle this complexity and the numerical issues that arise from the vast range of data values in real-life meat processing (from decagrams to tons), the researchers designed a clever iterative approach. This method is based on Integer Linear Programming (ILP), a mathematical technique for optimizing a linear objective function, subject to linear constraints, where some or all of the variables are restricted to be integers. The key advantage of their iterative strategy is that it only adds the complex MOQ and MPA constraints when they are absolutely necessary. This not only helps in mitigating numerical instability but also allows the problem to be solved efficiently using open-source ILP solvers, avoiding the need for expensive commercial software.
The effectiveness of this new algorithm was rigorously tested using real production data from a large meat processing company. The results were highly promising, demonstrating that the algorithm could find optimal solutions within a few seconds for all tested scenarios. This rapid solution time is crucial for production planners, enabling them to quickly adapt to changes in demand or other disruptions.
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The paper’s contributions are significant: it provides a robust mathematical model for a real-life production problem, complete with previously neglected constraints like MOQ and MPA. It offers a formal proof of the problem’s complexity and introduces an innovative iterative solution approach that is both numerically stable and compatible with accessible software. Furthermore, the experimental evaluation on real data provides practical insights into how objective weights and specific requirements impact the solution quality, helping companies optimize purchasing expenses and make informed decisions, such as determining the optimal number of hogs to slaughter. This research is a vital step towards enhancing the resilience and efficiency of the meat production sector. You can read the full paper here.
